Báo cáo toán học: " On Score Sets in Tournaments" pptx

... Yao, Reid’s conjecture on score sets in tournaments, Kexue Tongbao 33 (1988) 481–484 (in Chinese). 7. T. X. Yao, On Reid’s conjecture of score sets for tournaments, Chinese Sci. Bull. 34 (1989) ... of Reid’s conjecture by pure arithmetical analysis which appeared in Chinese [6] in 1988 and in English [7] in 1989. In the following result, we prove that any set of p non...

Ngày tải lên: 06/08/2014, 05:20

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Ngày tải lên: 05/08/2014, 15:20

... 1998 ABSTRACT An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128. 1. Introduction Let τ n denote the maximal kissing number in dimension n, that is, ... 1,260,230,400 in dimensions 32, 64 and 128, for example). In contrast, Quebbemann’s lattice Q 32 [14], [5, Chap. 8] has τ = 261,120. In recent years the kissing numbers of a f...

Ngày tải lên: 07/08/2014, 06:22

... exists, if certain necessary and sufficient conditions are met. The conditions in Theorem 1.1 are closely related to those given in the following result of Niessen and Randerath [5] on regular graphs. Theorem ... vertices into ∗ corresponding author the electronic journal of combinatorics 11 (2004), #R7 1 For regular graphs without a k-factor, for odd k, we can give the following result...

Ngày tải lên: 07/08/2014, 08:20

... them can have exponentially many vertices in terms of max F and |F|. The second construction from [6] does not even give one-realization of F.We present an algorithmic construction (Theorem 2) ... Note that the condition r 1 = 0 is the condition 1 ∈ F mentioned earlier. We generalize this theorem in Section 3. We prove that for each vector (r 1 , ,r m ) of non-negative integers such that...

Ngày tải lên: 07/08/2014, 08:20

... and contains at least one perfect dominating set, a set S ⊆ V (G) is a minimum dominating set if and only if it is a perfect dominating set. In [2] Chartrand et al. studied the size of defining sets ... analysis on Z n p . Section 3 is devoted to the proof of Theorem 2. Sec- tion 4 contains further discussions about the defining sets of minimum dominating sets of Γ(Z n 2n+1 , U). 2 Ba...

Ngày tải lên: 07/08/2014, 13:21

... 2.89319, a contradiction to our assumption. This proves Theorem 3.  We conclude with a remark on the explicit relation between α and β that we use here. Combining (16) with (14) and simplifying, we ... 3-cycle. In the next section, we cite the Chudnovsky–Seymour–Sullivan result and a conjecture of theirs, and derive a useful consequence. In Section 3, we outline Shen’s proof of his bou...

Ngày tải lên: 07/08/2014, 13:21

... r-identifying (in G) if the sets I r (v) are nonempty and pairwise different for all v ∈ V. In a closely related problem of r-locating-dominating sets, the sets I r (v) must also be nonempty and ... cardinalities for identifying and locating-dominating codes in graphs, Discrete Math., 307 (2007), pp. 356–366. [6] C. J. Colbourn, P. J. Slater and L. K. Stewart, Locating dominating se...

Ngày tải lên: 07/08/2014, 15:22

... (resp. increasing, de- creasing, concave, convex, log-concave, log-convex), then so is its subsequence {a n 0 +id } i≥0 for arbitrary fixed nonnegative integers n 0 and d. Proof. We only consider ... section, we prove Theorem 1. In Section 3, we present a combinatorial proof of the log-concavity in Theorem 1 (ii). In Section 4, we show more precise results about the asymptotically log-co...

Ngày tải lên: 07/08/2014, 21:20

... maximum independent set in C d k2 d +1 has exactly one hole in each 1-dimensional slice. Consequently, the intersection of S with each ℓ-dimensional slice projects onto a maximum independent set in ... length 2 in the d-dimensional torus of side length 2n+ 1 corresponds to an independent set in C d 2n+1 . (This correspondence between packings of cubes in the torus and independent...

Ngày tải lên: 07/08/2014, 21:21